large part a consumption puzzle: given the low volatility of consumption
growth, why are investors so reluctant to buy a high return asset, stocks,
especially when that asset’s covariance with consumption growth is so low?
Since BT do not consider an intertemporal model with consumption choice,
they cannot address this issue directly.
To see if prospect theory can in fact help with the equity premium puzzle,
Barberis, Huang, and Santos (2001), BHS henceforth, make a first attempt
at building it into a dynamic equilibrium model of stock returns. A simple
version of their model, an extension of which we consider later, examines
an economy with the same structure as the one described at the start of sec-
tion 4, but in which investors have the preferences
(11)The investor gets utility from consumption, but over and above that, he
gets utility from changes in the value of his holdings of the risky asset be-
tween tand t+1, denoted here by Xt+ 1. Motivated by BT’s findings, BHS
define the unit of time to be a year, so that gains and losses are measured
annually.
The utility from these gains and losses is determined by υˆwhere
(12)The 2.25 factor comes from Tversky and Kahneman’s (1992) experimental
study of attitudes to timeless gambles. This functional form is simpler than
the one used by BT, υ. It captures loss aversion, but ignores other elements
of prospect theory, such as the concavity (convexity) over gains (losses) and
the probability transformation. In part this is because it is difficult to incor-
porate all these features into a fully dynamic framework; but also, it is based
on BT’s observation that it is mainly loss aversion that drives their results.^17
BHS show that loss aversion can indeed provide a partial explanation of
the high Sharpe ratio on the aggregate stock market. However, how much
of the Sharpe ratio it can explain depends heavily on the importance of the
ˆ()
.for,
.υXX
XX
X=≥
<
^2250
0E
C
t t bCttX
t01
01
0 1ρ
γυγ
γ−
+
=∞−+
∑
ˆ().28 BARBERIS AND THALER
(^17) The coefficient on the loss aversion term is a scaling factor which ensures that risk
premia in the economy remain stationary even as aggregate wealth increases over time. It in-
volves per capita consumption which is exogeneous to the investor, and so does not affect
the intuition of the model. The constant b 0 controls the importance of the loss aversion term
in the investor’s preferences; setting b 0 =0 reduces the model to the much studied case of
power utility over consumption. As b 0 →∞, the investor’s decisions are driven primarily by
concern about gains and losses in financial wealth, as assumed by Benartzi and Thaler.
Ct
bC 0 tγ